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Simplifying 5d + -6a + 7d + 3a + -2 + 8a + 7 = 0 Reorder the terms: -2 + 7 + -6a + 3a + 8a + 5d + 7d = 0 Combine like terms: -2 + 7 = 5 5 + -6a + 3a + 8a + 5d + 7d = 0 Combine like terms: -6a + 3a = -3a 5 + -3a + 8a + 5d + 7d = 0 Combine like terms: -3a + 8a = 5a 5 + 5a + 5d + 7d = 0 Combine like terms: 5d + 7d = 12d 5 + 5a + 12d = 0 Solving 5 + 5a + 12d = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + 5a + -5 + 12d = 0 + -5 Reorder the terms: 5 + -5 + 5a + 12d = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 5a + 12d = 0 + -5 5a + 12d = 0 + -5 Combine like terms: 0 + -5 = -5 5a + 12d = -5 Add '-12d' to each side of the equation. 5a + 12d + -12d = -5 + -12d Combine like terms: 12d + -12d = 0 5a + 0 = -5 + -12d 5a = -5 + -12d Divide each side by '5'. a = -1 + -2.4d Simplifying a = -1 + -2.4d
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